Encyclopedia of Wireless Networks

Living Edition
| Editors: Xuemin (Sherman) Shen, Xiaodong Lin, Kuan Zhang

Incentive Mechanism for Crowdsourcing-Based Spectrum Measurement

  • Xiaoyan WangEmail author
  • Masahiro Umehira
  • Biao Han
  • Yusheng Ji
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-32903-1_213-1

Synonyms

Definitions

Spectrum measurement is of great importance to realize the dynamic spectrum sharing framework. To construct the spectrum database, spectrum measurement is needed which measures the power of the spectrum of desired signals. Generally, this operation is performed by dedicated equipments owned by the operators. Crowdsourcing the spectrum measurement tasks to the mobile users is a promising solution to improve the accuracy of the spectrum database in a cost-efficient way.

Background

With the tremendous increase of wireless devices and applications, there is a common belief that we are facing a severe shortage of spectrum resource for wireless communications in the near future. Currently, the spectrum resources below 6 GHz is almost fully allocated to primary users (PUs) in a static and exclusive way, which is highly inefficient. To solve the spectrum crunch, we need a paradigm shift from the static, exclusive-use framework toward a dynamic spectrum sharing framework between PUs and secondary users (SUs). One promising solution that is being widely investigated is to employ a spectrum occupancy database, which relies on propagation models to calculate the received signal strength (RSS) at any receiver location. Unfortunately, this model-based spectrum database is prone to offer inaccurate and stale spectrum availability in many circumstances, e.g., approximately 40–70% of available white space is wasted in New York City (Saeed et al., 2014).

To improve the spectrum database accuracy, real-time spectrum measurements could be incorporated into the quasi-static database. A basic approach is to deploy dedicated sensors uniformly over the region of interest (Phillips et al., 2012). However it suffers from the high cost for database operator. A practical alternative is to exploit crowdsourcing for the sensing task (Nika et al., 2014), i.e., recruiting users with mobile devices that are outfitted with spectrum sensors. However participating in a crowdsourcing task may incur additional bandwidth usage and energy consumption for mobile users, and thus rewards in the form of either money or resource are needed to encourage them to make contributions.

Incentive mechanism for crowdsourcing-based spectrum measurement has been firstly investigated by Ying et al. (2015). Their goal is to minimize the interpolation variance for all the spots of interest for a given budget. Both budget-free mechanism with a cardinality constraint and budget-feasible mechanism by using bisection method are proposed. Gao et al. (2016) proposed a game-theoretic model-based mechanism to incentivize the users with additional spectrum access opportunities. Specifically, a two-level game model is considered, in which the database conducts dynamic pricing in a first-level Stackelberg game and SUs strategically contribute to spectrum sensing in a second-level stochastic game. One limitation of these mechanisms (Ying et al., 2015; Gao et al., 2016) is that they do not take into consideration the heterogeneity of spots that needs to be augmented and thus cannot recruit users to meet distinct interpolation requirements. In Wang et al. (2017b) proposed a fine-grained incentive mechanism for sensing augmented spectrum database by utilizing auction model Wang et al. (2017a), where users sell their location-specific spectrum measurement to the database operator. Instead of trying to augment the whole spectrum database, the spectrum sensing is only conducted on spots with poor propagation model-based estimation. In Wang et al. (2017c) proposed a barter-like exchange model to incentivize the SUs by using spectrum access right. Based on this model, a truthful reverse auction approach is adopted to select the SUs and determine the individual access time in a computational efficient way. In Chen et al. (2017) proposed a reputation-based cooperative spectrum sensing incentive framework, where the cooperation stimulation problem is modeled as an indirect reciprocity game. In the proposed framework, SUs choose how to report their sensing results to the database center and gain reputations, based on which they can access a certain amount of vacant licensed channels in the future.

Crowdsourcing Augmented Spectrum Database

In the current propagation model-based spectrum database, the location-specific RSS is calculated based on the transceiver distance information. However, the accuracy of the database is low especially in the urban areas due to the influence of buildings. For the approaches that try to completely replace the propagation model-based database by using extensive real-time sensing results, its capital expenditure and operating cost are extremely high. To this end, crowdsourcing augmented spectrum database system is proposed (architecture is illustrated in Fig. 1), which consists of a centralized spectrum database and multiple distributed users with mobile devices that are outfitted with spectrum sensors. The calibration on RSS by using real-time sensing results could only be executed in spots with poor calculation accuracy (white spots in Fig. 1), and the rest of the areas still use the propagation model-based approach. By this method, the spectrum database accuracy could be improved with only a modest sensing effort. The spots that need crowdsourcing augmented could be separated out by using machine learning classifier, e.g., decision tree classifier in Chakraborty and Das (2014). Specifically, by exploring the features of distance from transmitter, received power, and line-of-sight (LOS) obstruction length, it is possible to learn where the database is likely to make inaccurate RSS calculations.
Fig. 1

Architecture of the crowdsourcing augmented spectrum database

However, it is unlikely that a crowdsourcing participant locates exactly at the spot that the system wants to augment. Generally, the RSS for a desired spot is interpolated by using sensing measurements that are collected from surrounding users. Kriging Cressie and Cassie (1993) shows superior performance among different interpolation techniques and thus is widely utilized. Kriging is a linear regression method which uses location-specific known values to predict the unknown value in desired location. Consider that there is a random field in two dimensions and the value of that field (e.g., RSS in this entry) at a point (xi, yi) is zi = z(xi, yi). Given the values at a set of locations \(\mathcal {N}=\{(x_1,y_1)\), (x2, y2), …, (xn, yn)}, Kriging could predict the unknown value at a new location \(\hat {(z_0)}\) from the weighted known values as follows:
$$\displaystyle \begin{aligned} \hat{z_0}=\sum_{i=1}^{n}{\lambda_i z_i}, \end{aligned} $$
(1)
where λi is the normalized weight, i.e., \(\sum _{i=1}^{n} {\lambda _i}=1\). The optimal weights λi are determined by minimizing the estimation variance, i.e.:
$$\displaystyle \begin{aligned} \min_{\lambda_i} {Var\left(\hat{z_0}-z_0\right)}. \end{aligned} $$
(2)
For the widely used ordinary Kriging (OK), it assumes zi is intrinsically stationary such as:
$$\displaystyle \begin{aligned} \begin{aligned} E[z_i]&=c \\ Var[z_i]&=\sigma^2. \end{aligned} \end{aligned} $$
(3)
Let \(\phi _{(x_0,y_0)}(\mathcal {N})\) denote the goal function in Eq. (2), which is the estimation variance at (x0, y0) by using the measurements at set \(\mathcal {N}\). By substituting Eq. (1) into it, the following formula could be obtained:
$$\displaystyle \begin{aligned} \begin{aligned} & \phi_{(x_0,y_0)}(\mathcal {N})=Var\left(\sum_{i=1}^{n}{\lambda_i z_i}-z_0\right) \\ & \ \ =\sum_{i=1}^{n}\sum_{j=1}^{n}\lambda_i \lambda_j C_{ij}-2\sum_{i=1}^{n}\lambda_i C_{i0}+C_{00}, \end{aligned} \end{aligned} $$
(4)
where Cij = Cov(zi, zj) and Cov() denotes the covariance function.
To find minimum \(\phi _{(x_0,y_0)}(\mathcal {N})\), a key function, namely, semivariogram γij, is introduced. γij models the variance between two points as a function of their distance. The theoretical semivariogram is represented by
$$\displaystyle \begin{aligned} \gamma_{ij}=\frac{1}{2} E\left[(z_i-z_j)^2\right]. \end{aligned} $$
(5)
Based on the OK assumption in Eq. (3), γij could be expressed as
$$\displaystyle \begin{aligned} \gamma_{ij}=\sigma^2-C_{ij}. \end{aligned} $$
(6)
Substituting Eq. (6) into Eq. (4), \(\phi _{(x_0,y_0)}(\mathcal {N})\) could be expressed by using semivariogram γij as
$$\displaystyle \begin{aligned} \phi_{(x_0,y_0)}(\mathcal {N}){=}2\sum_{i=1}^{n} \lambda_i \gamma_{i0}-\sum_{i=1}^{n} \sum_{j=1}^{n} \lambda_i \lambda_j \gamma_{ij} - \gamma_{00}. \end{aligned} $$
(7)
By using Lagrange multiplier method, the minimization problem in Eq. (7) leads to solve the following matrix equation: where μ is the Lagrange parameter. Obviously, the optimal weight λi could be obtained if semivariogram γij is known. In practice, γij is estimated from measurements and then fitted with empirical curve, e.g., exponential or spherical model. The minimized \(\phi _{(x_0,y_0)}(\mathcal {N})\) represents the estimation uncertainty at an unmeasured location (x0, y0) by using measurements at set \(\mathcal {N}\), which could be used as a criterion in incentive mechanism design.

Incentive Mechanism

In this subsection, we introduce two kinds of incentive mechanisms for crowdsourcing-based spectrum measurement by using monetary reward and barter-like resource exchange, respectively. The considered network consists of a set of mobile users \(\mathcal {N}\) with user index i, who knows its current location (xi, yi). The set of spots that needs to be augmented (i.e., interpolated) by sensing results is denoted by \(\mathcal {M}\) with spot index j. The result of interpolation is quantified by the Kriging estimation variance, e.g., the estimation variance at spot j by the interpolation of the user set \(\mathcal {N}\) is denoted as \(\phi _j(\mathcal {N})\). The spectrum database acquires the sensing data from users periodically. The set of spots that needs to be interpolated varies at each period. At the beginning of a period, the spectrum database announces a sensing request with the center frequency information. Notice that the request does not need to contain the location information of the spots. Upon receiving the request, interested user i competes for this crowdsourcing task by submitting its location information (xi, yi). The database selects a winner set \(\mathcal {W}\) (\(\mathcal {W} \subseteq \mathcal {N}\)) to perform the crowdsourcing, and accordingly the informed winners report their sensing measurements to the database.

Monetary Reward-Based Incentive Mechanism

While participating in crowdsourcing, there is a cost ci occurring to user i, which is related to the additional bandwidth usage and energy consumption. Notice that the cost is a private information and thus is only known by the user itself. If user could receive a monetary reward pi from the database which is higher than its cost ci, user i would have the incentive to participate in the crowdsourcing task. Therefore, based on the assumption that the users are rational, they are always trying to maximize their utility which could be defined as follows:
$$\displaystyle \begin{aligned} u_i=\left\{ \begin{aligned} & p_i - c_i,&i \in \mathcal {W} \\ & 0, & \text{otherwise}. \end{aligned} \right. \end{aligned} $$
(9)
In a fine-grained system, each augmented spot j may have an estimation quality requirement rj. rj could be quantified by the Kriging estimation variance, that is, spot j’s RSS needs to be interpolated with a maximum estimation variance rj. Therefore, the considered problem could be formulated as the following optimization problem:
$$\displaystyle \begin{gathered}{} \min_{i \in \mathcal {W}} c_i \\ \text{subject } \text{to } \quad \phi_j(\mathcal {W}) \leq r_j, \forall j \in \mathcal {M}. \end{gathered} $$
(10)
where the objective function is to minimize the total costs of the selected user set \(\mathcal {W}\) for crowdsourcing and the constraint function ensures that the quality requirement for each spot is met, i.e., the estimation variance at spot j by the interpolation of the winner set \(\phi _j(\mathcal {W})\) is no larger than j’s requirement. The considered minimization problem is equivalent to the subset selection problem, which is proven to be NP-hard. Therefore, it is impossible to compute the optimal set of selected users that minimizes the total costs in polynomial time.
To solve this problem in an efficient way, an auction-based mechanism could be used (Wang et al., 2017b). Specifically, the database acts as a buyer who wants to buy measurement data, and the users act as sellers. Along with the location information, interested users also send bid bi to the database, which may or may not be its real cost ci. The mechanism consists of two phases: winner selection and payment determination. Winner selection algorithm is based on the greedy heuristics that keeps selecting the next user with most cost-efficient contribution until all the spots’ requirements are met. The cost-efficient contribution of user i changes according to the current winner set \(\mathcal {W}\), which is defined as
$$\displaystyle \begin{aligned} \alpha_i(\mathcal {W})=\frac{m_i(\mathcal {W})}{b_i}, \end{aligned} $$
(11)
where bi is i’s bid and \(m_i(\mathcal {W})\) is i’s total weighted marginal contribution based on the current \(\mathcal {W}\). \(m_i(\mathcal {W})\) is calculated by
$$\displaystyle \begin{gathered}{} m_i(\mathcal {W})=\sum_{j \in \mathcal {M}}\frac{\max\left(\phi_j(\mathcal {W}),r_j\right)-\max\left(\phi_j(\mathcal {W}\cup \{i\}),r_j\right)}{r_j}, \end{gathered} $$
(12)
Here, the numerator \(\max \left (\phi _j(\mathcal {W}),r_j\right ) -\max \left (\phi _j(\mathcal {W}\cup \{i\}),r_j\right )\) could be regarded as the “marginal contribution” of user i to spot j under the current winner set \(\mathcal {W}\). And this marginal contribution is weighted by 1∕rj, i.e., the spot with small variance requirement has large weight.
To determine the payment, the key point is to find the maximum bid each winner can submit that allows it to win, i.e., critical payment. By using the critical payment, the auction mechanism could be proven to be truthful. Truthful is one of the most important properties that an auction mechanism desires, since in a truthful auction, bidding the true cost (bi = ci) is the dominant strategy regardless of other users’ strategies. Specifically, to find the critical payment for winner k, the payment determination algorithm repeats the winner selection algorithm for the user set without k, i.e., \(\mathcal {N}'=\mathcal {N}\setminus \{k\}\). In set \(\mathcal {N}'\), the mechanism finds the winner l′ who has the maximum \(\alpha _{l'}(\mathcal {W'})\) based on the current winner set \(\mathcal {W'}\). To let winner k replace winner l′, its cost-efficient contribution needs to be larger than that of l′, that is:
$$\displaystyle \begin{aligned} \frac{m_k(\mathcal {W'})}{b_k} > \frac{m_{l'}(\mathcal {W'})}{b_{l'}}. \end{aligned} $$
(13)
In other words, the maximum bid for winner k that lets it replace winner l′ is \(\frac {m_k(\mathcal {W'})}{m_{l'}(\mathcal {W'})}\cdot b_{l'}\). Eventually, the maximum of these values is used as the critical payment for k.

Barter-Like Resource Exchange-Based Incentive Mechanism

It is assumed that the database incentivize users by using a nonmonetary payment pi which is in the form of additional channel access time. And each user that participates the crowdsourcing task has a desired channel access time, which is denoted by ti. Notice that ti is a private information and thus is only known by the user itself. The length of each round that the database operator wants to collect new measurements is T, during which the selected users could share the channel access in a TDMA fashion. The rational user always tries to maximize its utility, which is defined as
$$\displaystyle \begin{aligned} u_i=\left\{ \begin{aligned} & p_i - t_i,&i \in \mathcal {W} \\ & 0, & \text{otherwise}. \end{aligned} \right. \end{aligned} $$
(14)
Therefore, the considered problem could be formulated as the following optimization problem:
$$\displaystyle \begin{aligned} \begin{gathered} \min_{\mathcal {W}} \sum_{j \in \mathcal {M}} {\phi_j(\mathcal {W})} \\ \text{subject } \text{to } \quad \sum_{i \in \mathcal {W}} {p_i} \leq T, \end{gathered} \end{aligned} $$
(15)
where the objective function is to minimize the total Kriging variance for spot set \(\mathcal {M}\) by the interpolation of selected winner set \(\mathcal {W}\), and the constraint ensures that the sum of the payment for winner set \(\mathcal {W}\) does not exceed the time interval T. Similar to Eq. (), this optimization problem is NP-hard, and an auction-based mechanism could solve it in an efficient way (Wang et al., 2017c).
The mechanism consists of three phases, i.e., winner selection, payment determination, and bidding threshold search. Winner selection algorithm is based on the greedy heuristics that keeps selecting the next user with highest contribution-bidding ratio until the total bids exceed the current bidding threshold. The bidding threshold is related to the time interval T, which could be found by employing a bisection searching method. The contribution-bidding ratio of user i based on the current winner set \(\mathcal {W}\) is defined as
$$\displaystyle \begin{aligned} \alpha_i(\mathcal {W})=\frac{c_i(\mathcal {W})}{b_i}, \end{aligned} $$
(16)
where bi is i’s bid and \(c_i(\mathcal {W})\) is i’s interpolation variance contribution based on the current \(\mathcal {W}\). \(c_i(\mathcal {W})\) is calculated by
$$\displaystyle \begin{aligned} c_i(\mathcal {W})=\sum_{j \in \mathcal {M}}\left(\phi_j(\mathcal {W})-\phi_j(\mathcal {W}\cup \{i\})\right). \end{aligned} $$
(17)
To find the critical payment for winner k, the winner selection algorithm for the user set without k is repeated, i.e., \(\mathcal {N}'=\mathcal {N}\setminus \{k\}\). In set \(\mathcal {N}'\), the winner k′ could be found who has the maximum \(\alpha _{k'}(\mathcal {W'})\) based on the current winner set \(\mathcal {W'}\). To let winner k replace winner k′, its contribution-bidding ratio needs to be larger than that of k′, that is:
$$\displaystyle \begin{aligned} \alpha_{k}(\mathcal {W'})=\frac{c_k(\mathcal {W'})}{b_k} > \alpha_{k'}(\mathcal {W'})=\frac{c_{k'}(\mathcal {W'})}{b_{k'}}. \end{aligned} $$
(18)
In other words, the maximum bid for winner k that lets it replace winner k′ is \(\frac {c_k(\mathcal {W'})}{c_{k'}(\mathcal {W'})}\cdot b_{k'}\). Eventually, after finishing the winner selection loop on user set \(\mathcal {N}'\), the maximum of these values is used as the critical payment for k.

In a truthful auction, generally the final total payments are larger than the sum of winners’ bids. The final total payment is constrained by the time interval T. However, it is impossible to use constraint T to control the winner selection process, since the payment is determined after the selection of winners. Therefore, it is required to define a bidding threshold H to control the winner selection loop, i.e., the sum of the bids for all winners should not exceed this threshold. Obviously, the bidding threshold is smaller than the time constraint T, and using a bisection searching method could find it. Specifically, a lower bound l and a upper bound u are used to narrow down the possible range of the bidding threshold, and a tolerance e is employed to stop the searching process.

Key Applications

The crowdsoucing-based spectrum measurements are crucial for the dynamic spectrum sharing. Due to the tremendous increasing of mobile data traffic, dynamic and efficient spectrum sharing mechanism is required. To realize interference protection and reuse the whitespace efficiently, an accurate spectrum database that using crowdsourced spectrum measurement is promising.

Cross-References

References

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xiaoyan Wang
    • 1
    Email author
  • Masahiro Umehira
    • 1
  • Biao Han
    • 2
  • Yusheng Ji
    • 3
  1. 1.Ibaraki UniversityHitachiJapan
  2. 2.National University of Defense TechnologyChangshaChina
  3. 3.National Institute of InformaticsTokyoJapan

Section editors and affiliations

  • Yusheng Ji
    • 1
  1. 1.Information Systems Architecture Research DivisionNational Institute of Informatics, JapanTokyoJapan